A class of nonlinear integrodifferential impulsive periodic systems of mixed type and optimal controls on Banach space

A class of nonlinear integrodifferential impulsive periodic systems of mixed type on Banach space is considered. Existence of periodic PC-mild solutions is proved. Existence of periodic optimal pairs of systems governed by nonlinear impulsive integrodifferential equations of mixed type is also presented. An example is given for demonstration.